src/HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
author blanchet
Thu May 12 15:29:19 2011 +0200 (2011-05-12)
changeset 42734 4a1fc1816dbb
parent 42731 2490e5e2f3f5
child 42742 369dfc819056
permissions -rw-r--r--
don't give weights to built-in symbols
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(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
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    Author:     Fabian Immler, TU Muenchen
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    Author:     Makarius
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    Author:     Jasmin Blanchette, TU Muenchen
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Translation of HOL to FOL for Sledgehammer.
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*)
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signature SLEDGEHAMMER_ATP_TRANSLATE =
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sig
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  type 'a fo_term = 'a ATP_Problem.fo_term
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  type formula_kind = ATP_Problem.formula_kind
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  type 'a problem = 'a ATP_Problem.problem
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  type locality = Sledgehammer_Filter.locality
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  datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
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  datatype type_level =
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    All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
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  datatype type_system =
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    Simple_Types of type_level |
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    Preds of polymorphism * type_level |
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    Tags of polymorphism * type_level
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  type translated_formula
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  val readable_names : bool Config.T
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  val fact_prefix : string
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  val conjecture_prefix : string
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  val predicator_base : string
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  val explicit_app_base : string
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  val type_pred_base : string
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  val tff_type_prefix : string
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  val type_sys_from_string : string -> type_system
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  val polymorphism_of_type_sys : type_system -> polymorphism
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  val level_of_type_sys : type_system -> type_level
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  val is_type_sys_virtually_sound : type_system -> bool
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  val is_type_sys_fairly_sound : type_system -> bool
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  val num_atp_type_args : theory -> type_system -> string -> int
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  val unmangled_const : string -> string * string fo_term list
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  val translate_atp_fact :
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    Proof.context -> bool -> (string * locality) * thm
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    -> translated_formula option * ((string * locality) * thm)
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  val prepare_atp_problem :
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    Proof.context -> formula_kind -> formula_kind -> type_system -> bool
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    -> term list -> term
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    -> (translated_formula option * ((string * 'a) * thm)) list
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    -> string problem * string Symtab.table * int * int
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       * (string * 'a) list vector
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  val atp_problem_weights : string problem -> (string * real) list
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end;
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structure Sledgehammer_ATP_Translate : SLEDGEHAMMER_ATP_TRANSLATE =
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struct
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open ATP_Problem
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open Metis_Translate
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open Sledgehammer_Util
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open Sledgehammer_Filter
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(* experimental *)
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val generate_useful_info = false
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(* Readable names are often much shorter, especially if types are mangled in
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   names. Also, the logic for generating legal SNARK sort names is only
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   implemented for readable names. Finally, readable names are, well, more
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   readable. For these reason, they are enabled by default. *)
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val readable_names =
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  Attrib.setup_config_bool @{binding sledgehammer_atp_readable_names} (K true)
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val type_decl_prefix = "type_"
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val sym_decl_prefix = "sym_"
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val fact_prefix = "fact_"
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val conjecture_prefix = "conj_"
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val helper_prefix = "help_"
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val class_rel_clause_prefix = "crel_";
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val arity_clause_prefix = "arity_"
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val tfree_prefix = "tfree_"
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val predicator_base = "hBOOL"
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val explicit_app_base = "hAPP"
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val type_pred_base = "is"
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val tff_type_prefix = "ty_"
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fun make_tff_type s = tff_type_prefix ^ ascii_of s
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(* Freshness almost guaranteed! *)
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val sledgehammer_weak_prefix = "Sledgehammer:"
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datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
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datatype type_level =
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  All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
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datatype type_system =
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  Simple_Types of type_level |
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  Preds of polymorphism * type_level |
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  Tags of polymorphism * type_level
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fun try_unsuffixes ss s =
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  fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
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fun type_sys_from_string s =
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  (case try (unprefix "poly_") s of
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     SOME s => (SOME Polymorphic, s)
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   | NONE =>
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     case try (unprefix "mono_") s of
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       SOME s => (SOME Monomorphic, s)
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     | NONE =>
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       case try (unprefix "mangled_") s of
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         SOME s => (SOME Mangled_Monomorphic, s)
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       | NONE => (NONE, s))
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  ||> (fn s =>
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          (* "_query" and "_bang" are for the ASCII-challenged Mirabelle. *)
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          case try_unsuffixes ["?", "_query"] s of
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            SOME s => (Nonmonotonic_Types, s)
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          | NONE =>
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            case try_unsuffixes ["!", "_bang"] s of
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              SOME s => (Finite_Types, s)
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            | NONE => (All_Types, s))
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  |> (fn (poly, (level, core)) =>
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         case (core, (poly, level)) of
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           ("simple_types", (NONE, level)) => Simple_Types level
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         | ("preds", (SOME poly, level)) => Preds (poly, level)
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         | ("tags", (SOME poly, level)) => Tags (poly, level)
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         | ("args", (SOME poly, All_Types (* naja *))) =>
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           Preds (poly, Const_Arg_Types)
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         | ("erased", (NONE, All_Types (* naja *))) =>
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           Preds (Polymorphic, No_Types)
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         | _ => error ("Unknown type system: " ^ quote s ^ "."))
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fun polymorphism_of_type_sys (Simple_Types _) = Mangled_Monomorphic
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  | polymorphism_of_type_sys (Preds (poly, _)) = poly
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  | polymorphism_of_type_sys (Tags (poly, _)) = poly
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fun level_of_type_sys (Simple_Types level) = level
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  | level_of_type_sys (Preds (_, level)) = level
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  | level_of_type_sys (Tags (_, level)) = level
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fun is_type_level_virtually_sound level =
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  level = All_Types orelse level = Nonmonotonic_Types
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val is_type_sys_virtually_sound =
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  is_type_level_virtually_sound o level_of_type_sys
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fun is_type_level_fairly_sound level =
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  is_type_level_virtually_sound level orelse level = Finite_Types
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val is_type_sys_fairly_sound = is_type_level_fairly_sound o level_of_type_sys
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fun is_type_level_partial level =
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  level = Nonmonotonic_Types orelse level = Finite_Types
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fun formula_map f (AQuant (q, xs, phi)) = AQuant (q, xs, formula_map f phi)
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  | formula_map f (AConn (c, phis)) = AConn (c, map (formula_map f) phis)
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  | formula_map f (AAtom tm) = AAtom (f tm)
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fun formula_fold pos f =
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  let
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    fun aux pos (AQuant (_, _, phi)) = aux pos phi
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      | aux pos (AConn (ANot, [phi])) = aux (Option.map not pos) phi
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      | aux pos (AConn (AImplies, [phi1, phi2])) =
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        aux (Option.map not pos) phi1 #> aux pos phi2
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      | aux pos (AConn (AAnd, phis)) = fold (aux pos) phis
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      | aux pos (AConn (AOr, phis)) = fold (aux pos) phis
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      | aux _ (AConn (_, phis)) = fold (aux NONE) phis
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      | aux pos (AAtom tm) = f pos tm
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  in aux (SOME pos) end
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type translated_formula =
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  {name: string,
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   locality: locality,
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   kind: formula_kind,
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   combformula: (name, typ, combterm) formula,
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   atomic_types: typ list}
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fun update_combformula f ({name, locality, kind, combformula, atomic_types}
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                          : translated_formula) =
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  {name = name, locality = locality, kind = kind, combformula = f combformula,
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   atomic_types = atomic_types} : translated_formula
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fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
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val boring_consts = [explicit_app_base, @{const_name Metis.fequal}]
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fun should_omit_type_args type_sys s =
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  s <> type_pred_base andalso s <> type_tag_name andalso
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  (s = @{const_name HOL.eq} orelse level_of_type_sys type_sys = No_Types orelse
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   (case type_sys of
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      Tags (_, All_Types) => true
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    | _ => polymorphism_of_type_sys type_sys <> Mangled_Monomorphic andalso
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           member (op =) boring_consts s))
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datatype type_arg_policy = No_Type_Args | Explicit_Type_Args | Mangled_Type_Args
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fun general_type_arg_policy type_sys =
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  if level_of_type_sys type_sys = No_Types then
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    No_Type_Args
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  else if polymorphism_of_type_sys type_sys = Mangled_Monomorphic then
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    Mangled_Type_Args
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  else
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    Explicit_Type_Args
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fun type_arg_policy type_sys s =
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  if should_omit_type_args type_sys s then No_Type_Args
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  else general_type_arg_policy type_sys
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fun num_atp_type_args thy type_sys s =
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  if type_arg_policy type_sys s = Explicit_Type_Args then num_type_args thy s
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  else 0
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fun atp_type_literals_for_types type_sys kind Ts =
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  if level_of_type_sys type_sys = No_Types then
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    []
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  else
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    Ts |> type_literals_for_types
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       |> filter (fn TyLitVar _ => kind <> Conjecture
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                   | TyLitFree _ => kind = Conjecture)
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fun mk_anot phi = AConn (ANot, [phi])
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fun mk_aconn c phi1 phi2 = AConn (c, [phi1, phi2])
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fun mk_aconns c phis =
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  let val (phis', phi') = split_last phis in
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    fold_rev (mk_aconn c) phis' phi'
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  end
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fun mk_ahorn [] phi = phi
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  | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
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fun mk_aquant _ [] phi = phi
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  | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
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    if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
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  | mk_aquant q xs phi = AQuant (q, xs, phi)
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fun close_universally atom_vars phi =
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  let
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    fun formula_vars bounds (AQuant (_, xs, phi)) =
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        formula_vars (map fst xs @ bounds) phi
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      | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
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      | formula_vars bounds (AAtom tm) =
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        union (op =) (atom_vars tm []
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                      |> filter_out (member (op =) bounds o fst))
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  in mk_aquant AForall (formula_vars [] phi []) phi end
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fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
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  | combterm_vars (CombConst _) = I
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  | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
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fun close_combformula_universally phi = close_universally combterm_vars phi
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fun term_vars (ATerm (name as (s, _), tms)) =
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  is_atp_variable s ? insert (op =) (name, NONE)
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  #> fold term_vars tms
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fun close_formula_universally phi = close_universally term_vars phi
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fun fo_term_from_typ (Type (s, Ts)) =
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    ATerm (`make_fixed_type_const s, map fo_term_from_typ Ts)
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  | fo_term_from_typ (TFree (s, _)) =
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    ATerm (`make_fixed_type_var s, [])
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  | fo_term_from_typ (TVar ((x as (s, _)), _)) =
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    ATerm ((make_schematic_type_var x, s), [])
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(* This shouldn't clash with anything else. *)
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val mangled_type_sep = "\000"
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fun generic_mangled_type_name f (ATerm (name, [])) = f name
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  | generic_mangled_type_name f (ATerm (name, tys)) =
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    f name ^ "(" ^ commas (map (generic_mangled_type_name f) tys) ^ ")"
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val mangled_type_name =
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  fo_term_from_typ
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  #> (fn ty => (make_tff_type (generic_mangled_type_name fst ty),
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                generic_mangled_type_name snd ty))
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fun generic_mangled_type_suffix f g Ts =
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  fold_rev (curry (op ^) o g o prefix mangled_type_sep
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            o generic_mangled_type_name f) Ts ""
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fun mangled_const_name T_args (s, s') =
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  let val ty_args = map fo_term_from_typ T_args in
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    (s ^ generic_mangled_type_suffix fst ascii_of ty_args,
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     s' ^ generic_mangled_type_suffix snd I ty_args)
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  end
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val parse_mangled_ident =
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  Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
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fun parse_mangled_type x =
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  (parse_mangled_ident
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   -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
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                    [] >> ATerm) x
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and parse_mangled_types x =
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  (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
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fun unmangled_type s =
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  s |> suffix ")" |> raw_explode
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    |> Scan.finite Symbol.stopper
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           (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
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                                                quote s)) parse_mangled_type))
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    |> fst
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val unmangled_const_name = space_explode mangled_type_sep #> hd
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fun unmangled_const s =
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  let val ss = space_explode mangled_type_sep s in
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    (hd ss, map unmangled_type (tl ss))
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  end
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fun introduce_proxies tm =
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  let
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    fun aux top_level (CombApp (tm1, tm2)) =
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        CombApp (aux top_level tm1, aux false tm2)
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      | aux top_level (CombConst (name as (s, s'), T, T_args)) =
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        (case proxify_const s of
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           SOME proxy_base =>
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           if top_level then
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             (case s of
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                "c_False" => (tptp_false, s')
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              | "c_True" => (tptp_true, s')
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              | _ => name, [])
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           else
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             (proxy_base |>> prefix const_prefix, T_args)
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          | NONE => (name, T_args))
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        |> (fn (name, T_args) => CombConst (name, T, T_args))
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      | aux _ tm = tm
blanchet@42674
   317
  in aux true tm end
blanchet@42568
   318
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   319
fun combformula_from_prop thy eq_as_iff =
blanchet@38282
   320
  let
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   321
    fun do_term bs t atomic_types =
blanchet@41140
   322
      combterm_from_term thy bs (Envir.eta_contract t)
blanchet@42568
   323
      |>> (introduce_proxies #> AAtom)
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   324
      ||> union (op =) atomic_types
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   325
    fun do_quant bs q s T t' =
blanchet@38518
   326
      let val s = Name.variant (map fst bs) s in
blanchet@38518
   327
        do_formula ((s, T) :: bs) t'
blanchet@42562
   328
        #>> mk_aquant q [(`make_bound_var s, SOME T)]
blanchet@38518
   329
      end
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   330
    and do_conn bs c t1 t2 =
blanchet@38282
   331
      do_formula bs t1 ##>> do_formula bs t2
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   332
      #>> uncurry (mk_aconn c)
blanchet@38282
   333
    and do_formula bs t =
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   334
      case t of
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   335
        @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
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   336
      | Const (@{const_name All}, _) $ Abs (s, T, t') =>
blanchet@38282
   337
        do_quant bs AForall s T t'
blanchet@38282
   338
      | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
blanchet@38282
   339
        do_quant bs AExists s T t'
haftmann@38795
   340
      | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
haftmann@38795
   341
      | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
haftmann@38786
   342
      | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
haftmann@38864
   343
      | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
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   344
        if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
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   345
      | _ => do_term bs t
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   346
  in do_formula [] end
blanchet@38282
   347
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   348
val presimplify_term = prop_of o Meson.presimplify oo Skip_Proof.make_thm
blanchet@38282
   349
wenzelm@41491
   350
fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
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   351
fun conceal_bounds Ts t =
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   352
  subst_bounds (map (Free o apfst concealed_bound_name)
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   353
                    (0 upto length Ts - 1 ~~ Ts), t)
blanchet@38282
   354
fun reveal_bounds Ts =
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   355
  subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
blanchet@38282
   356
                    (0 upto length Ts - 1 ~~ Ts))
blanchet@38282
   357
blanchet@38608
   358
(* Removes the lambdas from an equation of the form "t = (%x. u)".
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   359
   (Cf. "extensionalize_theorem" in "Meson_Clausify".) *)
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   360
fun extensionalize_term t =
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   361
  let
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   362
    fun aux j (@{const Trueprop} $ t') = @{const Trueprop} $ aux j t'
blanchet@38608
   363
      | aux j (t as Const (s, Type (_, [Type (_, [_, T']),
blanchet@38608
   364
                                        Type (_, [_, res_T])]))
blanchet@38608
   365
                    $ t2 $ Abs (var_s, var_T, t')) =
haftmann@38864
   366
        if s = @{const_name HOL.eq} orelse s = @{const_name "=="} then
blanchet@38608
   367
          let val var_t = Var ((var_s, j), var_T) in
blanchet@38608
   368
            Const (s, T' --> T' --> res_T)
blanchet@38608
   369
              $ betapply (t2, var_t) $ subst_bound (var_t, t')
blanchet@38608
   370
            |> aux (j + 1)
blanchet@38608
   371
          end
blanchet@38608
   372
        else
blanchet@38608
   373
          t
blanchet@38608
   374
      | aux _ t = t
blanchet@38608
   375
  in aux (maxidx_of_term t + 1) t end
blanchet@38608
   376
blanchet@38282
   377
fun introduce_combinators_in_term ctxt kind t =
wenzelm@42361
   378
  let val thy = Proof_Context.theory_of ctxt in
blanchet@38491
   379
    if Meson.is_fol_term thy t then
blanchet@38491
   380
      t
blanchet@38491
   381
    else
blanchet@38491
   382
      let
blanchet@38491
   383
        fun aux Ts t =
blanchet@38491
   384
          case t of
blanchet@38491
   385
            @{const Not} $ t1 => @{const Not} $ aux Ts t1
blanchet@38491
   386
          | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
blanchet@38491
   387
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   388
          | (t0 as Const (@{const_name All}, _)) $ t1 =>
blanchet@38652
   389
            aux Ts (t0 $ eta_expand Ts t1 1)
blanchet@38491
   390
          | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
blanchet@38491
   391
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   392
          | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
blanchet@38652
   393
            aux Ts (t0 $ eta_expand Ts t1 1)
haftmann@38795
   394
          | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38795
   395
          | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38786
   396
          | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38864
   397
          | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
blanchet@38491
   398
              $ t1 $ t2 =>
blanchet@38491
   399
            t0 $ aux Ts t1 $ aux Ts t2
blanchet@38491
   400
          | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
blanchet@38491
   401
                   t
blanchet@38491
   402
                 else
blanchet@38491
   403
                   t |> conceal_bounds Ts
blanchet@38491
   404
                     |> Envir.eta_contract
blanchet@38491
   405
                     |> cterm_of thy
blanchet@39890
   406
                     |> Meson_Clausify.introduce_combinators_in_cterm
blanchet@38491
   407
                     |> prop_of |> Logic.dest_equals |> snd
blanchet@38491
   408
                     |> reveal_bounds Ts
blanchet@39370
   409
        val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
blanchet@38491
   410
      in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
blanchet@38491
   411
      handle THM _ =>
blanchet@38491
   412
             (* A type variable of sort "{}" will make abstraction fail. *)
blanchet@38613
   413
             if kind = Conjecture then HOLogic.false_const
blanchet@38613
   414
             else HOLogic.true_const
blanchet@38491
   415
  end
blanchet@38282
   416
blanchet@38282
   417
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
blanchet@42353
   418
   same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
blanchet@38282
   419
fun freeze_term t =
blanchet@38282
   420
  let
blanchet@38282
   421
    fun aux (t $ u) = aux t $ aux u
blanchet@38282
   422
      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
blanchet@38282
   423
      | aux (Var ((s, i), T)) =
blanchet@38282
   424
        Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
blanchet@38282
   425
      | aux t = t
blanchet@38282
   426
  in t |> exists_subterm is_Var t ? aux end
blanchet@38282
   427
blanchet@40204
   428
(* making fact and conjecture formulas *)
blanchet@42640
   429
fun make_formula ctxt eq_as_iff presimp name loc kind t =
blanchet@38282
   430
  let
wenzelm@42361
   431
    val thy = Proof_Context.theory_of ctxt
blanchet@38608
   432
    val t = t |> Envir.beta_eta_contract
blanchet@38652
   433
              |> transform_elim_term
blanchet@41211
   434
              |> Object_Logic.atomize_term thy
blanchet@42563
   435
    val need_trueprop = (fastype_of t = @{typ bool})
blanchet@38652
   436
    val t = t |> need_trueprop ? HOLogic.mk_Trueprop
blanchet@38282
   437
              |> extensionalize_term
blanchet@38282
   438
              |> presimp ? presimplify_term thy
blanchet@38282
   439
              |> perhaps (try (HOLogic.dest_Trueprop))
blanchet@38282
   440
              |> introduce_combinators_in_term ctxt kind
blanchet@38613
   441
              |> kind <> Axiom ? freeze_term
blanchet@42562
   442
    val (combformula, atomic_types) =
blanchet@42562
   443
      combformula_from_prop thy eq_as_iff t []
blanchet@38282
   444
  in
blanchet@42640
   445
    {name = name, locality = loc, kind = kind, combformula = combformula,
blanchet@42562
   446
     atomic_types = atomic_types}
blanchet@38282
   447
  end
blanchet@38282
   448
blanchet@42640
   449
fun make_fact ctxt keep_trivial eq_as_iff presimp ((name, loc), t) =
blanchet@42640
   450
  case (keep_trivial, make_formula ctxt eq_as_iff presimp name loc Axiom t) of
blanchet@41990
   451
    (false, {combformula = AAtom (CombConst (("c_True", _), _, _)), ...}) =>
blanchet@41990
   452
    NONE
blanchet@41990
   453
  | (_, formula) => SOME formula
blanchet@42561
   454
blanchet@42709
   455
fun make_conjecture ctxt prem_kind ts =
blanchet@38613
   456
  let val last = length ts - 1 in
blanchet@42709
   457
    map2 (fn j => fn t =>
blanchet@42709
   458
             let
blanchet@42709
   459
               val (kind, maybe_negate) =
blanchet@42709
   460
                 if j = last then
blanchet@42709
   461
                   (Conjecture, I)
blanchet@42709
   462
                 else
blanchet@42709
   463
                   (prem_kind,
blanchet@42709
   464
                    if prem_kind = Conjecture then update_combformula mk_anot
blanchet@42709
   465
                    else I)
blanchet@42709
   466
              in
blanchet@42709
   467
                make_formula ctxt true true (string_of_int j) Chained kind t
blanchet@42709
   468
                |> maybe_negate
blanchet@42709
   469
              end)
blanchet@38613
   470
         (0 upto last) ts
blanchet@38613
   471
  end
blanchet@38282
   472
blanchet@42682
   473
(** Finite and infinite type inference **)
blanchet@42682
   474
blanchet@42682
   475
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
blanchet@42682
   476
   dangerous because their "exhaust" properties can easily lead to unsound ATP
blanchet@42682
   477
   proofs. On the other hand, all HOL infinite types can be given the same
blanchet@42682
   478
   models in first-order logic (via Löwenheim-Skolem). *)
blanchet@42682
   479
blanchet@42682
   480
fun should_encode_type _ _ All_Types _ = true
blanchet@42682
   481
  | should_encode_type ctxt _ Finite_Types T = is_type_surely_finite ctxt T
blanchet@42682
   482
  | should_encode_type _ nonmono_Ts Nonmonotonic_Types T =
blanchet@42682
   483
    exists (curry Type.raw_instance T) nonmono_Ts
blanchet@42682
   484
  | should_encode_type _ _ _ _ = false
blanchet@42682
   485
blanchet@42682
   486
fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level)) T =
blanchet@42682
   487
    should_encode_type ctxt nonmono_Ts level T
blanchet@42682
   488
  | should_predicate_on_type _ _ _ _ = false
blanchet@42682
   489
blanchet@42682
   490
fun should_tag_with_type ctxt nonmono_Ts (Tags (_, level)) T =
blanchet@42682
   491
    should_encode_type ctxt nonmono_Ts level T
blanchet@42682
   492
  | should_tag_with_type _ _ _ _ = false
blanchet@42682
   493
blanchet@42682
   494
val homo_infinite_T = @{typ ind} (* any infinite type *)
blanchet@42682
   495
blanchet@42682
   496
fun homogenized_type ctxt nonmono_Ts level T =
blanchet@42682
   497
  if should_encode_type ctxt nonmono_Ts level T then T else homo_infinite_T
blanchet@42682
   498
blanchet@42573
   499
(** "hBOOL" and "hAPP" **)
blanchet@41313
   500
blanchet@42574
   501
type sym_info =
blanchet@42563
   502
  {pred_sym : bool, min_ary : int, max_ary : int, typ : typ option}
blanchet@42563
   503
blanchet@42574
   504
fun add_combterm_syms_to_table explicit_apply =
blanchet@42558
   505
  let
blanchet@42558
   506
    fun aux top_level tm =
blanchet@42558
   507
      let val (head, args) = strip_combterm_comb tm in
blanchet@42558
   508
        (case head of
blanchet@42563
   509
           CombConst ((s, _), T, _) =>
blanchet@42558
   510
           if String.isPrefix bound_var_prefix s then
blanchet@42558
   511
             I
blanchet@42558
   512
           else
blanchet@42563
   513
             let val ary = length args in
blanchet@42558
   514
               Symtab.map_default
blanchet@42558
   515
                   (s, {pred_sym = true,
blanchet@42563
   516
                        min_ary = if explicit_apply then 0 else ary,
blanchet@42563
   517
                        max_ary = 0, typ = SOME T})
blanchet@42563
   518
                   (fn {pred_sym, min_ary, max_ary, typ} =>
blanchet@42558
   519
                       {pred_sym = pred_sym andalso top_level,
blanchet@42563
   520
                        min_ary = Int.min (ary, min_ary),
blanchet@42563
   521
                        max_ary = Int.max (ary, max_ary),
blanchet@42563
   522
                        typ = if typ = SOME T then typ else NONE})
blanchet@42558
   523
            end
blanchet@42558
   524
         | _ => I)
blanchet@42558
   525
        #> fold (aux false) args
blanchet@42558
   526
      end
blanchet@42558
   527
  in aux true end
blanchet@42674
   528
fun add_fact_syms_to_table explicit_apply =
blanchet@42680
   529
  fact_lift (formula_fold true (K (add_combterm_syms_to_table explicit_apply)))
blanchet@38282
   530
blanchet@42675
   531
val default_sym_table_entries : (string * sym_info) list =
blanchet@42563
   532
  [("equal", {pred_sym = true, min_ary = 2, max_ary = 2, typ = NONE}),
blanchet@42568
   533
   (make_fixed_const predicator_base,
blanchet@42563
   534
    {pred_sym = true, min_ary = 1, max_ary = 1, typ = NONE})] @
blanchet@42568
   535
  ([tptp_false, tptp_true]
blanchet@42563
   536
   |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, typ = NONE}))
blanchet@41140
   537
blanchet@42544
   538
fun sym_table_for_facts explicit_apply facts =
blanchet@42568
   539
  Symtab.empty |> fold Symtab.default default_sym_table_entries
blanchet@42574
   540
               |> fold (add_fact_syms_to_table explicit_apply) facts
blanchet@38282
   541
blanchet@42558
   542
fun min_arity_of sym_tab s =
blanchet@42558
   543
  case Symtab.lookup sym_tab s of
blanchet@42574
   544
    SOME ({min_ary, ...} : sym_info) => min_ary
blanchet@42558
   545
  | NONE =>
blanchet@42558
   546
    case strip_prefix_and_unascii const_prefix s of
blanchet@42547
   547
      SOME s =>
blanchet@42570
   548
      let val s = s |> unmangled_const_name |> invert_const in
blanchet@42568
   549
        if s = predicator_base then 1
blanchet@42547
   550
        else if s = explicit_app_base then 2
blanchet@42547
   551
        else if s = type_pred_base then 1
blanchet@42557
   552
        else 0
blanchet@42547
   553
      end
blanchet@42544
   554
    | NONE => 0
blanchet@38282
   555
blanchet@38282
   556
(* True if the constant ever appears outside of the top-level position in
blanchet@38282
   557
   literals, or if it appears with different arities (e.g., because of different
blanchet@38282
   558
   type instantiations). If false, the constant always receives all of its
blanchet@38282
   559
   arguments and is used as a predicate. *)
blanchet@42558
   560
fun is_pred_sym sym_tab s =
blanchet@42558
   561
  case Symtab.lookup sym_tab s of
blanchet@42574
   562
    SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
blanchet@42574
   563
    pred_sym andalso min_ary = max_ary
blanchet@42558
   564
  | NONE => false
blanchet@38282
   565
blanchet@42568
   566
val predicator_combconst =
blanchet@42568
   567
  CombConst (`make_fixed_const predicator_base, @{typ "bool => bool"}, [])
blanchet@42568
   568
fun predicator tm = CombApp (predicator_combconst, tm)
blanchet@42542
   569
blanchet@42568
   570
fun introduce_predicators_in_combterm sym_tab tm =
blanchet@42542
   571
  case strip_combterm_comb tm of
blanchet@42542
   572
    (CombConst ((s, _), _, _), _) =>
blanchet@42568
   573
    if is_pred_sym sym_tab s then tm else predicator tm
blanchet@42568
   574
  | _ => predicator tm
blanchet@42542
   575
blanchet@42544
   576
fun list_app head args = fold (curry (CombApp o swap)) args head
blanchet@42544
   577
blanchet@42544
   578
fun explicit_app arg head =
blanchet@42544
   579
  let
blanchet@42562
   580
    val head_T = combtyp_of head
blanchet@42693
   581
    val (arg_T, res_T) = dest_funT head_T
blanchet@42544
   582
    val explicit_app =
blanchet@42562
   583
      CombConst (`make_fixed_const explicit_app_base, head_T --> head_T,
blanchet@42693
   584
                 [arg_T, res_T])
blanchet@42544
   585
  in list_app explicit_app [head, arg] end
blanchet@42544
   586
fun list_explicit_app head args = fold explicit_app args head
blanchet@38282
   587
blanchet@42565
   588
fun introduce_explicit_apps_in_combterm sym_tab =
blanchet@42544
   589
  let
blanchet@42544
   590
    fun aux tm =
blanchet@42544
   591
      case strip_combterm_comb tm of
blanchet@42544
   592
        (head as CombConst ((s, _), _, _), args) =>
blanchet@42544
   593
        args |> map aux
blanchet@42557
   594
             |> chop (min_arity_of sym_tab s)
blanchet@42544
   595
             |>> list_app head
blanchet@42544
   596
             |-> list_explicit_app
blanchet@42544
   597
      | (head, args) => list_explicit_app head (map aux args)
blanchet@42544
   598
  in aux end
blanchet@38282
   599
blanchet@42701
   600
fun impose_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys =
blanchet@42573
   601
  let
blanchet@42573
   602
    fun aux (CombApp tmp) = CombApp (pairself aux tmp)
blanchet@42574
   603
      | aux (CombConst (name as (s, _), T, T_args)) =
blanchet@42701
   604
        let
blanchet@42701
   605
          val level = level_of_type_sys type_sys
blanchet@42701
   606
          val (T, T_args) =
blanchet@42701
   607
            (* Aggressively merge most "hAPPs" if the type system is unsound
blanchet@42701
   608
               anyway, by distinguishing overloads only on the homogenized
blanchet@42701
   609
               result type. *)
blanchet@42701
   610
            if s = const_prefix ^ explicit_app_base andalso
blanchet@42726
   611
               length T_args = 2 andalso
blanchet@42701
   612
               not (is_type_sys_virtually_sound type_sys) then
blanchet@42701
   613
              T_args |> map (homogenized_type ctxt nonmono_Ts level)
blanchet@42701
   614
                     |> (fn Ts => let val T = hd Ts --> nth Ts 1 in
blanchet@42701
   615
                                    (T --> T, tl Ts)
blanchet@42701
   616
                                  end)
blanchet@42701
   617
            else
blanchet@42701
   618
              (T, T_args)
blanchet@42701
   619
        in
blanchet@42701
   620
          (case strip_prefix_and_unascii const_prefix s of
blanchet@42701
   621
             NONE => (name, T_args)
blanchet@42701
   622
           | SOME s'' =>
blanchet@42701
   623
             let val s'' = invert_const s'' in
blanchet@42701
   624
               case type_arg_policy type_sys s'' of
blanchet@42701
   625
                 No_Type_Args => (name, [])
blanchet@42701
   626
               | Explicit_Type_Args => (name, T_args)
blanchet@42701
   627
               | Mangled_Type_Args => (mangled_const_name T_args name, [])
blanchet@42701
   628
             end)
blanchet@42701
   629
          |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@42701
   630
        end
blanchet@42573
   631
      | aux tm = tm
blanchet@42573
   632
  in aux end
blanchet@42573
   633
blanchet@42701
   634
fun repair_combterm ctxt nonmono_Ts type_sys sym_tab =
blanchet@42565
   635
  introduce_explicit_apps_in_combterm sym_tab
blanchet@42568
   636
  #> introduce_predicators_in_combterm sym_tab
blanchet@42701
   637
  #> impose_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42701
   638
fun repair_fact ctxt nonmono_Ts type_sys sym_tab =
blanchet@42701
   639
  update_combformula (formula_map
blanchet@42701
   640
      (repair_combterm ctxt nonmono_Ts type_sys sym_tab))
blanchet@42573
   641
blanchet@42573
   642
(** Helper facts **)
blanchet@42573
   643
blanchet@42573
   644
fun ti_ti_helper_fact () =
blanchet@42573
   645
  let
blanchet@42573
   646
    fun var s = ATerm (`I s, [])
blanchet@42589
   647
    fun tag tm = ATerm (`make_fixed_const type_tag_name, [var "X", tm])
blanchet@42573
   648
  in
blanchet@42612
   649
    Formula (helper_prefix ^ "ti_ti", Axiom,
blanchet@42573
   650
             AAtom (ATerm (`I "equal", [tag (tag (var "Y")), tag (var "Y")]))
blanchet@42573
   651
             |> close_formula_universally, NONE, NONE)
blanchet@42573
   652
  end
blanchet@42573
   653
blanchet@42574
   654
fun helper_facts_for_sym ctxt type_sys (s, {typ, ...} : sym_info) =
blanchet@42573
   655
  case strip_prefix_and_unascii const_prefix s of
blanchet@42573
   656
    SOME mangled_s =>
blanchet@42573
   657
    let
blanchet@42573
   658
      val thy = Proof_Context.theory_of ctxt
blanchet@42573
   659
      val unmangled_s = mangled_s |> unmangled_const_name
blanchet@42579
   660
      fun dub_and_inst c needs_some_types (th, j) =
blanchet@42579
   661
        ((c ^ "_" ^ string_of_int j ^ (if needs_some_types then "T" else ""),
blanchet@42640
   662
          Chained),
blanchet@42573
   663
         let val t = th |> prop_of in
blanchet@42589
   664
           t |> (general_type_arg_policy type_sys = Mangled_Type_Args andalso
blanchet@42573
   665
                 not (null (Term.hidden_polymorphism t)))
blanchet@42573
   666
                ? (case typ of
blanchet@42573
   667
                     SOME T => specialize_type thy (invert_const unmangled_s, T)
blanchet@42573
   668
                   | NONE => I)
blanchet@42573
   669
         end)
blanchet@42573
   670
      fun make_facts eq_as_iff =
blanchet@42573
   671
        map_filter (make_fact ctxt false eq_as_iff false)
blanchet@42589
   672
      val has_some_types = is_type_sys_fairly_sound type_sys
blanchet@42573
   673
    in
blanchet@42573
   674
      metis_helpers
blanchet@42579
   675
      |> maps (fn (metis_s, (needs_some_types, ths)) =>
blanchet@42573
   676
                  if metis_s <> unmangled_s orelse
blanchet@42589
   677
                     (needs_some_types andalso not has_some_types) then
blanchet@42573
   678
                    []
blanchet@42573
   679
                  else
blanchet@42573
   680
                    ths ~~ (1 upto length ths)
blanchet@42579
   681
                    |> map (dub_and_inst mangled_s needs_some_types)
blanchet@42579
   682
                    |> make_facts (not needs_some_types))
blanchet@42573
   683
    end
blanchet@42573
   684
  | NONE => []
blanchet@42573
   685
fun helper_facts_for_sym_table ctxt type_sys sym_tab =
blanchet@42573
   686
  Symtab.fold_rev (append o helper_facts_for_sym ctxt type_sys) sym_tab []
blanchet@42573
   687
blanchet@42573
   688
fun translate_atp_fact ctxt keep_trivial =
blanchet@42573
   689
  `(make_fact ctxt keep_trivial true true o apsnd prop_of)
blanchet@42573
   690
blanchet@42709
   691
fun translate_formulas ctxt prem_kind type_sys hyp_ts concl_t rich_facts =
blanchet@42573
   692
  let
blanchet@42573
   693
    val thy = Proof_Context.theory_of ctxt
blanchet@42573
   694
    val fact_ts = map (prop_of o snd o snd) rich_facts
blanchet@42573
   695
    val (facts, fact_names) =
blanchet@42573
   696
      rich_facts
blanchet@42573
   697
      |> map_filter (fn (NONE, _) => NONE
blanchet@42573
   698
                      | (SOME fact, (name, _)) => SOME (fact, name))
blanchet@42573
   699
      |> ListPair.unzip
blanchet@42573
   700
    (* Remove existing facts from the conjecture, as this can dramatically
blanchet@42573
   701
       boost an ATP's performance (for some reason). *)
blanchet@42573
   702
    val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
blanchet@42573
   703
    val goal_t = Logic.list_implies (hyp_ts, concl_t)
blanchet@42573
   704
    val all_ts = goal_t :: fact_ts
blanchet@42573
   705
    val subs = tfree_classes_of_terms all_ts
blanchet@42573
   706
    val supers = tvar_classes_of_terms all_ts
blanchet@42573
   707
    val tycons = type_consts_of_terms thy all_ts
blanchet@42709
   708
    val conjs = make_conjecture ctxt prem_kind (hyp_ts @ [concl_t])
blanchet@42573
   709
    val (supers', arity_clauses) =
blanchet@42589
   710
      if level_of_type_sys type_sys = No_Types then ([], [])
blanchet@42573
   711
      else make_arity_clauses thy tycons supers
blanchet@42573
   712
    val class_rel_clauses = make_class_rel_clauses thy subs supers'
blanchet@42573
   713
  in
blanchet@42573
   714
    (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
blanchet@42573
   715
  end
blanchet@42573
   716
blanchet@42573
   717
fun fo_literal_from_type_literal (TyLitVar (class, name)) =
blanchet@42573
   718
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   719
  | fo_literal_from_type_literal (TyLitFree (class, name)) =
blanchet@42573
   720
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   721
blanchet@42573
   722
fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
blanchet@42573
   723
blanchet@42701
   724
fun type_pred_combatom ctxt nonmono_Ts type_sys T tm =
blanchet@42573
   725
  CombApp (CombConst (`make_fixed_const type_pred_base, T --> @{typ bool}, [T]),
blanchet@42573
   726
           tm)
blanchet@42701
   727
  |> impose_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42573
   728
  |> AAtom
blanchet@42573
   729
blanchet@42680
   730
fun formula_from_combformula ctxt nonmono_Ts type_sys =
blanchet@42573
   731
  let
blanchet@42589
   732
    fun tag_with_type type_sys T tm =
blanchet@42589
   733
      CombConst (`make_fixed_const type_tag_name, T --> T, [T])
blanchet@42701
   734
      |> impose_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42589
   735
      |> do_term true
blanchet@42589
   736
      |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
blanchet@42589
   737
    and do_term top_level u =
blanchet@42573
   738
      let
blanchet@42573
   739
        val (head, args) = strip_combterm_comb u
blanchet@42574
   740
        val (x, T_args) =
blanchet@42573
   741
          case head of
blanchet@42574
   742
            CombConst (name, _, T_args) => (name, T_args)
blanchet@42573
   743
          | CombVar (name, _) => (name, [])
blanchet@42573
   744
          | CombApp _ => raise Fail "impossible \"CombApp\""
blanchet@42574
   745
        val t = ATerm (x, map fo_term_from_typ T_args @
blanchet@42573
   746
                          map (do_term false) args)
blanchet@42574
   747
        val T = combtyp_of u
blanchet@42573
   748
      in
blanchet@42680
   749
        t |> (if not top_level andalso
blanchet@42680
   750
                should_tag_with_type ctxt nonmono_Ts type_sys T then
blanchet@42589
   751
                tag_with_type type_sys T
blanchet@42573
   752
              else
blanchet@42573
   753
                I)
blanchet@42573
   754
      end
blanchet@42573
   755
    val do_bound_type =
blanchet@42682
   756
      case type_sys of
blanchet@42722
   757
        Simple_Types level =>
blanchet@42682
   758
        SOME o mangled_type_name o homogenized_type ctxt nonmono_Ts level
blanchet@42682
   759
      | _ => K NONE
blanchet@42573
   760
    fun do_out_of_bound_type (s, T) =
blanchet@42680
   761
      if should_predicate_on_type ctxt nonmono_Ts type_sys T then
blanchet@42701
   762
        type_pred_combatom ctxt nonmono_Ts type_sys T (CombVar (s, T))
blanchet@42573
   763
        |> do_formula |> SOME
blanchet@42573
   764
      else
blanchet@42573
   765
        NONE
blanchet@42573
   766
    and do_formula (AQuant (q, xs, phi)) =
blanchet@42573
   767
        AQuant (q, xs |> map (apsnd (fn NONE => NONE
blanchet@42574
   768
                                      | SOME T => do_bound_type T)),
blanchet@42573
   769
                (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
blanchet@42573
   770
                    (map_filter
blanchet@42573
   771
                         (fn (_, NONE) => NONE
blanchet@42574
   772
                           | (s, SOME T) => do_out_of_bound_type (s, T)) xs)
blanchet@42573
   773
                    (do_formula phi))
blanchet@42573
   774
      | do_formula (AConn (c, phis)) = AConn (c, map do_formula phis)
blanchet@42573
   775
      | do_formula (AAtom tm) = AAtom (do_term true tm)
blanchet@42573
   776
  in do_formula end
blanchet@42573
   777
blanchet@42727
   778
fun bound_atomic_types type_sys Ts =
blanchet@42727
   779
  mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
blanchet@42727
   780
                (atp_type_literals_for_types type_sys Axiom Ts))
blanchet@42727
   781
blanchet@42680
   782
fun formula_for_fact ctxt nonmono_Ts type_sys
blanchet@42573
   783
                     ({combformula, atomic_types, ...} : translated_formula) =
blanchet@42727
   784
  combformula
blanchet@42727
   785
  |> close_combformula_universally
blanchet@42727
   786
  |> formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42727
   787
  |> bound_atomic_types type_sys atomic_types
blanchet@42573
   788
  |> close_formula_universally
blanchet@42573
   789
blanchet@42640
   790
fun useful_isabelle_info s = SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
blanchet@42640
   791
blanchet@42573
   792
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
blanchet@42573
   793
   of monomorphization). The TPTP explicitly forbids name clashes, and some of
blanchet@42573
   794
   the remote provers might care. *)
blanchet@42680
   795
fun formula_line_for_fact ctxt prefix nonmono_Ts type_sys
blanchet@42640
   796
                          (j, formula as {name, locality, kind, ...}) =
blanchet@42680
   797
  Formula (prefix ^ (if polymorphism_of_type_sys type_sys = Polymorphic then ""
blanchet@42680
   798
                     else string_of_int j ^ "_") ^
blanchet@42647
   799
           ascii_of name,
blanchet@42680
   800
           kind, formula_for_fact ctxt nonmono_Ts type_sys formula, NONE,
blanchet@42640
   801
           if generate_useful_info then
blanchet@42640
   802
             case locality of
blanchet@42640
   803
               Intro => useful_isabelle_info "intro"
blanchet@42640
   804
             | Elim => useful_isabelle_info "elim"
blanchet@42640
   805
             | Simp => useful_isabelle_info "simp"
blanchet@42640
   806
             | _ => NONE
blanchet@42640
   807
           else
blanchet@42640
   808
             NONE)
blanchet@42573
   809
blanchet@42573
   810
fun formula_line_for_class_rel_clause (ClassRelClause {name, subclass,
blanchet@42573
   811
                                                       superclass, ...}) =
blanchet@42573
   812
  let val ty_arg = ATerm (`I "T", []) in
blanchet@42577
   813
    Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   814
             AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
blanchet@42573
   815
                               AAtom (ATerm (superclass, [ty_arg]))])
blanchet@42573
   816
             |> close_formula_universally, NONE, NONE)
blanchet@42573
   817
  end
blanchet@42573
   818
blanchet@42573
   819
fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
blanchet@42573
   820
    (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
blanchet@42573
   821
  | fo_literal_from_arity_literal (TVarLit (c, sort)) =
blanchet@42573
   822
    (false, ATerm (c, [ATerm (sort, [])]))
blanchet@42573
   823
blanchet@42573
   824
fun formula_line_for_arity_clause (ArityClause {name, conclLit, premLits,
blanchet@42573
   825
                                                ...}) =
blanchet@42577
   826
  Formula (arity_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   827
           mk_ahorn (map (formula_from_fo_literal o apfst not
blanchet@42573
   828
                          o fo_literal_from_arity_literal) premLits)
blanchet@42573
   829
                    (formula_from_fo_literal
blanchet@42573
   830
                         (fo_literal_from_arity_literal conclLit))
blanchet@42573
   831
           |> close_formula_universally, NONE, NONE)
blanchet@42573
   832
blanchet@42680
   833
fun formula_line_for_conjecture ctxt nonmono_Ts type_sys
blanchet@42573
   834
        ({name, kind, combformula, ...} : translated_formula) =
blanchet@42577
   835
  Formula (conjecture_prefix ^ name, kind,
blanchet@42680
   836
           formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42573
   837
                                    (close_combformula_universally combformula)
blanchet@42573
   838
           |> close_formula_universally, NONE, NONE)
blanchet@42573
   839
blanchet@42573
   840
fun free_type_literals type_sys ({atomic_types, ...} : translated_formula) =
blanchet@42573
   841
  atomic_types |> atp_type_literals_for_types type_sys Conjecture
blanchet@42573
   842
               |> map fo_literal_from_type_literal
blanchet@42573
   843
blanchet@42573
   844
fun formula_line_for_free_type j lit =
blanchet@42577
   845
  Formula (tfree_prefix ^ string_of_int j, Hypothesis,
blanchet@42573
   846
           formula_from_fo_literal lit, NONE, NONE)
blanchet@42573
   847
fun formula_lines_for_free_types type_sys facts =
blanchet@42573
   848
  let
blanchet@42573
   849
    val litss = map (free_type_literals type_sys) facts
blanchet@42573
   850
    val lits = fold (union (op =)) litss []
blanchet@42573
   851
  in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
blanchet@42573
   852
blanchet@42573
   853
(** Symbol declarations **)
blanchet@42544
   854
blanchet@42677
   855
fun insert_type get_T x xs =
blanchet@42677
   856
  let val T = get_T x in
blanchet@42677
   857
    if exists (curry Type.raw_instance T o get_T) xs then xs
blanchet@42677
   858
    else x :: filter_out ((fn T' => Type.raw_instance (T', T)) o get_T) xs
blanchet@42677
   859
  end
blanchet@42677
   860
blanchet@42574
   861
fun should_declare_sym type_sys pred_sym s =
blanchet@42542
   862
  not (String.isPrefix bound_var_prefix s) andalso s <> "equal" andalso
blanchet@42645
   863
  not (String.isPrefix "$" s) andalso
blanchet@42722
   864
  ((case type_sys of Simple_Types _ => true | _ => false) orelse not pred_sym)
blanchet@38282
   865
blanchet@42698
   866
fun sym_decl_table_for_facts type_sys repaired_sym_tab (conjs, facts) =
blanchet@42574
   867
  let
blanchet@42698
   868
    fun add_combterm in_conj tm =
blanchet@42574
   869
      let val (head, args) = strip_combterm_comb tm in
blanchet@42574
   870
        (case head of
blanchet@42574
   871
           CombConst ((s, s'), T, T_args) =>
blanchet@42574
   872
           let val pred_sym = is_pred_sym repaired_sym_tab s in
blanchet@42574
   873
             if should_declare_sym type_sys pred_sym s then
blanchet@42576
   874
               Symtab.map_default (s, [])
blanchet@42698
   875
                   (insert_type #3 (s', T_args, T, pred_sym, length args,
blanchet@42698
   876
                                    in_conj))
blanchet@42574
   877
             else
blanchet@42574
   878
               I
blanchet@42574
   879
           end
blanchet@42574
   880
         | _ => I)
blanchet@42698
   881
        #> fold (add_combterm in_conj) args
blanchet@42574
   882
      end
blanchet@42698
   883
    fun add_fact in_conj =
blanchet@42698
   884
      fact_lift (formula_fold true (K (add_combterm in_conj)))
blanchet@42698
   885
  in
blanchet@42698
   886
    Symtab.empty
blanchet@42698
   887
    |> is_type_sys_fairly_sound type_sys
blanchet@42698
   888
       ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
blanchet@42698
   889
  end
blanchet@42533
   890
blanchet@42677
   891
fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
blanchet@42677
   892
    String.isPrefix bound_var_prefix s
blanchet@42677
   893
  | is_var_or_bound_var (CombVar _) = true
blanchet@42677
   894
  | is_var_or_bound_var _ = false
blanchet@42677
   895
blanchet@42685
   896
(* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
blanchet@42685
   897
   out with monotonicity" paper presented at CADE 2011. *)
blanchet@42680
   898
fun add_combterm_nonmonotonic_types _ (SOME false) _ = I
blanchet@42680
   899
  | add_combterm_nonmonotonic_types ctxt _
blanchet@42680
   900
        (CombApp (CombApp (CombConst (("equal", _), Type (_, [T, _]), _), tm1),
blanchet@42680
   901
                  tm2)) =
blanchet@42680
   902
    (exists is_var_or_bound_var [tm1, tm2] andalso
blanchet@42680
   903
     not (is_type_surely_infinite ctxt T)) ? insert_type I T
blanchet@42680
   904
  | add_combterm_nonmonotonic_types _ _ _ = I
blanchet@42680
   905
fun add_fact_nonmonotonic_types ctxt ({kind, combformula, ...}
blanchet@42680
   906
                                      : translated_formula) =
blanchet@42680
   907
  formula_fold (kind <> Conjecture) (add_combterm_nonmonotonic_types ctxt)
blanchet@42680
   908
               combformula
blanchet@42680
   909
fun add_nonmonotonic_types_for_facts ctxt type_sys facts =
blanchet@42680
   910
  level_of_type_sys type_sys = Nonmonotonic_Types
blanchet@42731
   911
  ? (fold (add_fact_nonmonotonic_types ctxt) facts
blanchet@42731
   912
     (* in case helper "True_or_False" is included *)
blanchet@42731
   913
     #> insert_type I @{typ bool})
blanchet@42677
   914
blanchet@42574
   915
fun n_ary_strip_type 0 T = ([], T)
blanchet@42574
   916
  | n_ary_strip_type n (Type (@{type_name fun}, [dom_T, ran_T])) =
blanchet@42574
   917
    n_ary_strip_type (n - 1) ran_T |>> cons dom_T
blanchet@42574
   918
  | n_ary_strip_type _ _ = raise Fail "unexpected non-function"
blanchet@42533
   919
blanchet@42698
   920
fun result_type_of_decl (_, _, T, _, ary, _) = n_ary_strip_type ary T |> snd
blanchet@42579
   921
blanchet@42698
   922
fun decl_line_for_sym s (s', _, T, pred_sym, ary, _) =
blanchet@42579
   923
  let val (arg_Ts, res_T) = n_ary_strip_type ary T in
blanchet@42612
   924
    Decl (sym_decl_prefix ^ s, (s, s'), map mangled_type_name arg_Ts,
blanchet@42579
   925
          if pred_sym then `I tptp_tff_bool_type else mangled_type_name res_T)
blanchet@42579
   926
  end
blanchet@42579
   927
blanchet@42592
   928
fun is_polymorphic_type T = fold_atyps (fn TVar _ => K true | _ => I) T false
blanchet@42592
   929
blanchet@42709
   930
fun formula_line_for_sym_decl ctxt conj_sym_kind nonmono_Ts type_sys n s j
blanchet@42698
   931
                              (s', T_args, T, _, ary, in_conj) =
blanchet@42579
   932
  let
blanchet@42709
   933
    val (kind, maybe_negate) =
blanchet@42709
   934
      if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@42709
   935
      else (Axiom, I)
blanchet@42579
   936
    val (arg_Ts, res_T) = n_ary_strip_type ary T
blanchet@42579
   937
    val bound_names =
blanchet@42579
   938
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42579
   939
    val bound_tms =
blanchet@42579
   940
      bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
blanchet@42579
   941
    val bound_Ts =
blanchet@42592
   942
      arg_Ts |> map (fn T => if n > 1 orelse is_polymorphic_type T then SOME T
blanchet@42592
   943
                             else NONE)
blanchet@42579
   944
  in
blanchet@42612
   945
    Formula (sym_decl_prefix ^ s ^
blanchet@42709
   946
             (if n > 1 then "_" ^ string_of_int j else ""), kind,
blanchet@42579
   947
             CombConst ((s, s'), T, T_args)
blanchet@42579
   948
             |> fold (curry (CombApp o swap)) bound_tms
blanchet@42701
   949
             |> type_pred_combatom ctxt nonmono_Ts type_sys res_T
blanchet@42579
   950
             |> mk_aquant AForall (bound_names ~~ bound_Ts)
blanchet@42680
   951
             |> formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42727
   952
             |> n > 1 ? bound_atomic_types type_sys (atyps_of T)
blanchet@42709
   953
             |> close_formula_universally
blanchet@42709
   954
             |> maybe_negate,
blanchet@42579
   955
             NONE, NONE)
blanchet@42579
   956
  end
blanchet@42579
   957
blanchet@42709
   958
fun problem_lines_for_sym_decls ctxt conj_sym_kind nonmono_Ts type_sys
blanchet@42709
   959
                                (s, decls) =
blanchet@42682
   960
  case type_sys of
blanchet@42722
   961
    Simple_Types _ => map (decl_line_for_sym s) decls
blanchet@42682
   962
  | _ =>
blanchet@42574
   963
    let
blanchet@42579
   964
      val decls =
blanchet@42579
   965
        case decls of
blanchet@42579
   966
          decl :: (decls' as _ :: _) =>
blanchet@42592
   967
          let val T = result_type_of_decl decl in
blanchet@42592
   968
            if forall ((fn T' => Type.raw_instance (T', T))
blanchet@42592
   969
                       o result_type_of_decl) decls' then
blanchet@42592
   970
              [decl]
blanchet@42592
   971
            else
blanchet@42592
   972
              decls
blanchet@42592
   973
          end
blanchet@42579
   974
        | _ => decls
blanchet@42579
   975
      val n = length decls
blanchet@42579
   976
      val decls =
blanchet@42680
   977
        decls |> filter (should_predicate_on_type ctxt nonmono_Ts type_sys
blanchet@42579
   978
                         o result_type_of_decl)
blanchet@42574
   979
    in
blanchet@42709
   980
      (0 upto length decls - 1, decls)
blanchet@42709
   981
      |-> map2 (formula_line_for_sym_decl ctxt conj_sym_kind nonmono_Ts type_sys
blanchet@42709
   982
                                          n s)
blanchet@42574
   983
    end
blanchet@42579
   984
blanchet@42709
   985
fun problem_lines_for_sym_decl_table ctxt conj_sym_kind nonmono_Ts type_sys
blanchet@42709
   986
                                     sym_decl_tab =
blanchet@42709
   987
  Symtab.fold_rev (append o problem_lines_for_sym_decls ctxt conj_sym_kind
blanchet@42709
   988
                                                        nonmono_Ts type_sys)
blanchet@42574
   989
                  sym_decl_tab []
blanchet@42543
   990
blanchet@42543
   991
fun add_tff_types_in_formula (AQuant (_, xs, phi)) =
blanchet@42543
   992
    union (op =) (map_filter snd xs) #> add_tff_types_in_formula phi
blanchet@42543
   993
  | add_tff_types_in_formula (AConn (_, phis)) =
blanchet@42543
   994
    fold add_tff_types_in_formula phis
blanchet@42543
   995
  | add_tff_types_in_formula (AAtom _) = I
blanchet@42539
   996
blanchet@42562
   997
fun add_tff_types_in_problem_line (Decl (_, _, arg_Ts, res_T)) =
blanchet@42562
   998
    union (op =) (res_T :: arg_Ts)
blanchet@42577
   999
  | add_tff_types_in_problem_line (Formula (_, _, phi, _, _)) =
blanchet@42543
  1000
    add_tff_types_in_formula phi
blanchet@42543
  1001
blanchet@42543
  1002
fun tff_types_in_problem problem =
blanchet@42543
  1003
  fold (fold add_tff_types_in_problem_line o snd) problem []
blanchet@42543
  1004
blanchet@42545
  1005
fun decl_line_for_tff_type (s, s') =
blanchet@42568
  1006
  Decl (type_decl_prefix ^ ascii_of s, (s, s'), [], `I tptp_tff_type_of_types)
blanchet@42543
  1007
blanchet@42543
  1008
val type_declsN = "Types"
blanchet@42544
  1009
val sym_declsN = "Symbol types"
blanchet@41157
  1010
val factsN = "Relevant facts"
blanchet@41157
  1011
val class_relsN = "Class relationships"
blanchet@42543
  1012
val aritiesN = "Arities"
blanchet@41157
  1013
val helpersN = "Helper facts"
blanchet@41157
  1014
val conjsN = "Conjectures"
blanchet@41313
  1015
val free_typesN = "Type variables"
blanchet@41157
  1016
blanchet@41157
  1017
fun offset_of_heading_in_problem _ [] j = j
blanchet@41157
  1018
  | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
blanchet@41157
  1019
    if heading = needle then j
blanchet@41157
  1020
    else offset_of_heading_in_problem needle problem (j + length lines)
blanchet@41157
  1021
blanchet@42709
  1022
fun prepare_atp_problem ctxt conj_sym_kind prem_kind type_sys explicit_apply
blanchet@42709
  1023
                        hyp_ts concl_t facts =
blanchet@38282
  1024
  let
blanchet@41313
  1025
    val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
blanchet@42709
  1026
      translate_formulas ctxt prem_kind type_sys hyp_ts concl_t facts
blanchet@42563
  1027
    val sym_tab = conjs @ facts |> sym_table_for_facts explicit_apply
blanchet@42682
  1028
    val nonmono_Ts =
blanchet@42682
  1029
      [] |> fold (add_nonmonotonic_types_for_facts ctxt type_sys) [facts, conjs]
blanchet@42701
  1030
    val repair = repair_fact ctxt nonmono_Ts type_sys sym_tab
blanchet@42682
  1031
    val (conjs, facts) = (conjs, facts) |> pairself (map repair)
blanchet@42680
  1032
    val repaired_sym_tab = conjs @ facts |> sym_table_for_facts false
blanchet@42573
  1033
    val helpers =
blanchet@42682
  1034
      repaired_sym_tab |> helper_facts_for_sym_table ctxt type_sys |> map repair
blanchet@42680
  1035
    val sym_decl_lines =
blanchet@42731
  1036
      (conjs, helpers @ facts)
blanchet@42680
  1037
      |> sym_decl_table_for_facts type_sys repaired_sym_tab
blanchet@42709
  1038
      |> problem_lines_for_sym_decl_table ctxt conj_sym_kind nonmono_Ts type_sys
blanchet@42522
  1039
    (* Reordering these might confuse the proof reconstruction code or the SPASS
blanchet@42522
  1040
       Flotter hack. *)
blanchet@38282
  1041
    val problem =
blanchet@42561
  1042
      [(sym_declsN, sym_decl_lines),
blanchet@42680
  1043
       (factsN, map (formula_line_for_fact ctxt fact_prefix nonmono_Ts type_sys)
blanchet@42180
  1044
                    (0 upto length facts - 1 ~~ facts)),
blanchet@42545
  1045
       (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
blanchet@42545
  1046
       (aritiesN, map formula_line_for_arity_clause arity_clauses),
blanchet@42680
  1047
       (helpersN, map (formula_line_for_fact ctxt helper_prefix nonmono_Ts
blanchet@42680
  1048
                                             type_sys)
blanchet@42563
  1049
                      (0 upto length helpers - 1 ~~ helpers)
blanchet@42579
  1050
                  |> (case type_sys of
blanchet@42589
  1051
                        Tags (Polymorphic, level) =>
blanchet@42687
  1052
                        is_type_level_partial level
blanchet@42589
  1053
                        ? cons (ti_ti_helper_fact ())
blanchet@42579
  1054
                      | _ => I)),
blanchet@42680
  1055
       (conjsN, map (formula_line_for_conjecture ctxt nonmono_Ts type_sys)
blanchet@42680
  1056
                    conjs),
blanchet@42545
  1057
       (free_typesN, formula_lines_for_free_types type_sys (facts @ conjs))]
blanchet@42543
  1058
    val problem =
blanchet@42561
  1059
      problem
blanchet@42682
  1060
      |> (case type_sys of
blanchet@42722
  1061
            Simple_Types _ =>
blanchet@42561
  1062
            cons (type_declsN,
blanchet@42561
  1063
                  map decl_line_for_tff_type (tff_types_in_problem problem))
blanchet@42682
  1064
          | _ => I)
blanchet@42646
  1065
    val (problem, pool) =
blanchet@42646
  1066
      problem |> nice_atp_problem (Config.get ctxt readable_names)
blanchet@38282
  1067
  in
blanchet@38282
  1068
    (problem,
blanchet@38282
  1069
     case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
blanchet@42585
  1070
     offset_of_heading_in_problem conjsN problem 0,
blanchet@42541
  1071
     offset_of_heading_in_problem factsN problem 0,
blanchet@41157
  1072
     fact_names |> Vector.fromList)
blanchet@38282
  1073
  end
blanchet@38282
  1074
blanchet@41313
  1075
(* FUDGE *)
blanchet@41313
  1076
val conj_weight = 0.0
blanchet@41770
  1077
val hyp_weight = 0.1
blanchet@41770
  1078
val fact_min_weight = 0.2
blanchet@41313
  1079
val fact_max_weight = 1.0
blanchet@42608
  1080
val type_info_default_weight = 0.8
blanchet@41313
  1081
blanchet@41313
  1082
fun add_term_weights weight (ATerm (s, tms)) =
blanchet@42734
  1083
  (not (is_atp_variable s) andalso s <> "equal" andalso
blanchet@42734
  1084
   not (String.isPrefix "$" s)) ? Symtab.default (s, weight)
blanchet@41313
  1085
  #> fold (add_term_weights weight) tms
blanchet@42577
  1086
fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
blanchet@42680
  1087
    formula_fold true (K (add_term_weights weight)) phi
blanchet@42528
  1088
  | add_problem_line_weights _ _ = I
blanchet@41313
  1089
blanchet@41313
  1090
fun add_conjectures_weights [] = I
blanchet@41313
  1091
  | add_conjectures_weights conjs =
blanchet@41313
  1092
    let val (hyps, conj) = split_last conjs in
blanchet@41313
  1093
      add_problem_line_weights conj_weight conj
blanchet@41313
  1094
      #> fold (add_problem_line_weights hyp_weight) hyps
blanchet@41313
  1095
    end
blanchet@41313
  1096
blanchet@41313
  1097
fun add_facts_weights facts =
blanchet@41313
  1098
  let
blanchet@41313
  1099
    val num_facts = length facts
blanchet@41313
  1100
    fun weight_of j =
blanchet@41313
  1101
      fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
blanchet@41313
  1102
                        / Real.fromInt num_facts
blanchet@41313
  1103
  in
blanchet@41313
  1104
    map weight_of (0 upto num_facts - 1) ~~ facts
blanchet@41313
  1105
    |> fold (uncurry add_problem_line_weights)
blanchet@41313
  1106
  end
blanchet@41313
  1107
blanchet@41313
  1108
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
blanchet@41313
  1109
fun atp_problem_weights problem =
blanchet@42608
  1110
  let val get = these o AList.lookup (op =) problem in
blanchet@42608
  1111
    Symtab.empty
blanchet@42608
  1112
    |> add_conjectures_weights (get free_typesN @ get conjsN)
blanchet@42608
  1113
    |> add_facts_weights (get factsN)
blanchet@42608
  1114
    |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
blanchet@42608
  1115
            [sym_declsN, class_relsN, aritiesN]
blanchet@42608
  1116
    |> Symtab.dest
blanchet@42608
  1117
    |> sort (prod_ord Real.compare string_ord o pairself swap)
blanchet@42608
  1118
  end
blanchet@41313
  1119
blanchet@38282
  1120
end;